In [1]}, [2]}, [3]}, [4]}, [5]}, [6]} continuous and discontinuous protocols with finite-time convergence were proposed. However, the convergence-time is an unbounded function of the initial conditions. A remarkable extension of the previous methods is the fixed-time convergent consensus. In this case, there exists a bound for the convergence time that is independent of the initial conditions [7]}, [8]}. Therefore, for the design of high-performance consensus protocols, the fixed-time convergence is a desirable property. Several consensus protocol have been proposed based on the fixed-time stability results from [8]}, [10]}, see e.g., [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}. However, these consensus protocols have been justified only for static networks. Another fixed-time consensus algorithm was proposed by [18]}, which is a consensus protocol for dynamic networks. However, similar to [14]}, [15]}, the convergence analysis is based on the upper estimate of the convergence-time given in [8]}, which is known to be a too conservative upper bound [22]}.
